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HyperplaneArrangements :: subArrangement

subArrangement -- Subarrangement containing a fixed flat

Synopsis

Description

If X is the linear subspace indexed by the flat F, then the subarrangement A_F consists of those hyperplanes in A that contain X.
i1 : A := typeA(3)

o1 = {x  - x , x  - x , x  - x , x  - x , x  - x , x  - x }
       1    2   1    3   1    4   2    3   2    4   3    4

o1 : Hyperplane Arrangement 
i2 : flats(2,A)

o2 = {{0, 1, 3}, {0, 2, 4}, {0, 5}, {1, 4}, {1, 2, 5}, {2, 3}, {3, 4, 5}}

o2 : List
i3 : B := subArrangement first oo

o3 = {x  - x , x  - x , x  - x }
       1    2   1    3   2    3

o3 : Hyperplane Arrangement 
Note that the ambient vector space of A_F is the same as that of A; subarrangements are essential in general.
i4 : ring B

o4 = QQ[x ..x ]
         1   4

o4 : PolynomialRing

See also

Ways to use subArrangement :

For the programmer

The object subArrangement is a method function.